Question

In triangle ABC, cos A =
7
25
. Which other expression has a value of
7
25
?
A) sin B
B) tan B
C) cos B
D) tan A
E) tan C

Answer 1

The other expression that has a value of $\frac{7}{25}$ is A) sin B.

Step-by-step explanation:

Step 1:

$sin\theta = \frac{oppositeside}{hypotenuse} ,$ $cos\theta = \frac{adjacentside}{hypotenuse} ,$ $tan \theta = \frac{opposite side}{adjacent side} .$

For angle B, the opposite side measures 7 units, the adjacent side measures 24 units and the hypotenuse measures 25 units.

$sinB= \frac{oppositeside}{hypotenuse} = \frac{7}{25} ,$ $tan B = \frac{opposite side}{adjacent side} = \frac{7}{24} ,$ $cosB = \frac{adjacentside}{hypotenuse} = \frac{24}{25}.$

Step 2:

For angle A, the opposite side measures 24 units, the adjacent side measures 7 units and the hypotenuse measures 25 units.

$tan A = \frac{opposite side}{adjacent side} = \frac{24}{25} .$

Step 3:

tan C cannot be determined as C is the right angle. The opposite side and hypotenuse of the triangle would be the same.

So sin B also has a value of $\frac{7}{25}.$ This is option A.